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Science · Advanced Physics
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1. Consider an ideal Fermi gas at zero temperature. The density of states for this system is 2/3 ựJE , where EF-3NT is the Fermi energy at 7-0. 3 N g(E)- (a) Using the above facts and the Fermi-Dirac distribution, obtain the equation of state relating the pressure P, volume V, and particle number N of the gas at zero temperature. (b) Assume the valence electrons in sodium are free and constitute an ideal Fermi gas. Given a mass density of 0.95 g/cm3 and atomic weight of 23 for sodium, estimate (order of magnitude) the pressure in atmospheres that the free electrons exert on the lattice which confines them within the metal Electron mass: -9.10x10 1.01x10 erg/cm) g; Planck constant: h 6.63x10 erg-sec; 1 atm-

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